While most U.S. workers are satisfied with their health insurance benefits, their level of satisfaction is declining and they are increasingly concerned about costs, according to a recent survey.

The Employee Benefit Research Institute's 2015 Health and Voluntary Workplace Benefits Survey found that 66 percent of the 1,500 workers it polled were happy with their employer-based health plans. That's a slight drop from in 2014, when it was 69 percent, and the 74 percent who were satisfied in 2012 and 2013.

Shifting satisfaction rates could be traced to the fact that while employer-based plans aren't going away as some had predicted, they are changing amid the shifts brought on by health reform and other major trends in the healthcare industry.

Other findings from the survey include:

More employees in 2015 than in 2014 (44 percent compared to 40 percent) said they would prefer to continue to have their employers choose and pay for health insurance the way they do now.

Thirty-nine percent would prefer to choose their plan, have their employer pay the same amount it currently spends toward that insurance, then pay the remaining amounts themselves; 17 percent would rather their employer to give them the money and allow the workers to decide whether to purchase coverage and how much to spend.

More employees than in years past (20 percent) said they'd rather have fewer health benefits and higher wages. That share was 19 percent in 2014, 14 percent in 2013 and 10 percent in 2012.

Slightly more employees would trade higher wages for more health benefits in 2015 than in 2014 (14 percent compared to 12 percent). Yet "there appears to be a longer-term trend toward a reduction in the still-strong preference for health benefits over wages," the survey results say.

The largest share--79 percent--said premiums were the most important factor when choosing a health plan, followed closely by deductibles and co-payments (76 percent). Fifty-three percent, meanwhile, cited provider networks as the most important factor, while only 24 percent cited independent quality measures.